not sure why is this in the shitty admiral pool though
He leaves her to cry, being so desperate about how he might die from something not even remotely hurt (well no, it seriously hurts, just sometime). He might actually see it as it's better to let her see he's not dying because of that to give her a chance to stop being so desperate about small cuts too though. People just like to jump the gun and assume for the worst these days.
I get the impression even if the admiral wanted to, there is no way he could stop her without resorting to knocking her out or something. only way she will stop is for the wound to stop bleeding on its own.
shitty admiral isn't really fitting, especially considering the tags in the original picture, one of which is "addiction", which seems to imply yamakaze became "addicted(yandere)" to the admiral, the comment section seem to reinforce that as well.
It is characterized by at least 3 of the following:
1. encouraging or allowing others to make most of one's important life decisions; 2. subordination of one's own needs to those of others on whom one is dependent, and undue compliance with their wishes; 3. unwillingness to make even reasonable demands on the people one depends on; 4. feeling uncomfortable or helpless when alone, because of exaggerated fears of inability to care for oneself; 5. preoccupation with fears of being abandoned by a person with whom one has a close relationship, and of being left to care for oneself; 6. limited capacity to make everyday decisions without an excessive amount of advice and reassurance from others.
Associated features may include perceiving oneself as helpless, incompetent, and lacking stamina.
Includes:
asthenic, inadequate, passive, and self-defeating personality (disorder)
These two in conjunction would result in someone who has an obsessive need for positive emotional validation from anyone close to her, especially authority figures, while at the same time having a fear of negative feedback so utterly crippling she also tries to drive everyone away to prevent such a thing from happening. (Basically, she is terrified of abandonment, while also desiring abandonment because of a fear of disappointing anyone, resulting in an obsession for and against the concept of abandonment... it's not exactly the most stable of personalities.)
Beyond that, if one gets over the initial avoidance to the dependence, she would be almost fully reliant for all decisions upon those she is dependent upon, preferring to abnegate all responsibility for decisions, and measuring her worth directly in terms of how much she has helped the one she is dependent upon. Because the dependent person feels no sense of self-worth on their own, only when they are being fed praise from outside, it essentially causes something not unlike "addiction"; They're drowning in negativity on their own, and only get fed positive feelings with those people they have developed dependency upon. To keep getting at that positive feedback, they have to keep doing everything they possibly can to get praise from the people they depend upon. The Avoidant edge to that would push her towards hysterical assumptions of bad outcomes.
(In fact, minus the Avoidant Personality Disorder, you could match up Ikazuchi's fanon neurosis with Dependent Personality Disorder.)
The exact facts are a little fuzzy because of fanon discrepencies with one another, but you could totally write this as a genuine psychological condition if one were well-enough versed in the topic and had a desire to do so... It would then be a question of whether or not you wanted to make a strip all about therapy, or if you wanted to just show them being "comically" dysfunctional.
In any event, the right answer depends on the strategy for dealing with the dependent personality. Saying "Oh, look, it's stopping, thanks for saving me, Yamakaze, you're such a wonderful help," would positively reinforce the cycle of dependence, although it would also sate the withdrawl...
Updated
A-ah...! I need to... stop the bleeding fast... Stop the... bleeding...Stop... stop already... please stop...!No... Nooo!!I don't want that!How about saying something to her?Well,Is that so?seeing her trying so hard like this is kinda, you know...With that injury?Nah, it's just a paper cut.The Admiral's... going to die... noo...!!A-aaah...! I have to hurry... or the admiral will die...